MP TET 2020: Study Notes on Circle

Circle: A circle is a set of all those points in a plane whose distance from a fixed point remains constant.

Circle Properties:

Some of the important properties of the circle are as follows:

• The circles are said to be congruent if they have equal radii
• The diameter of a circle is the longest chord of a circle
• Equal chords and equal circles have an equal circumference
• The radius drawn perpendicular to the chord bisects the chord
• Circles having different radii are similar.

Circle Formulas:

• Area of a circle, A = πr² square units
• The circumference of a circle = 2πr units
• The circumference of a circle formula is also written as πd
• Where, Diameter = 2 x Radius, D = 2r, Here “r” represents the radius of a circle.

Let us learn some important facts about the circle:

• The path traced by a moving point is called the circumference of the circle.
• The fixed point is the centre of the circle and the fixed distance from a fixed point to any point on the circumference is called the radius.
• Diameter = 2 X Radius
• Radius = (Diameter / 2).

Radius: The radius of a circle is the distance between all the points of the circle to its centre.

Centre: The centre of a circle is a fixed point that is at a constant distance from all the points.

Diameter: A line segment passing through the centre of a circle, and having its end-points on the circle is called a diameter of the circle.

Chord: A line segment with its end-points lying on a circle is called the chord of the circle.

 Interior of a circle: The part of a plane inside the circle consisting of all the points is called the interior of a circle.

Circumference: The distance around a rectangle or a square is as you might remember called the perimeter. The distance around a circle on the other hand is called the circumference. Circumference (or) perimeter of a circle = 2πR

PRACTICE TIME

1. A circle of radius r cm has a diameter of length
(a) r cm
(b) 2r cm
(c) 4r cm
(d) r/2 cm

Solution:

Option (b) is the correct answer.

A circle of radius r cm has a diameter of length of 2r cm.

2. A chord of a circle passing through its centre is equal to its
(a) radius
(b) diameter
(c) circumference
(d) none of these

Solution:

Option (b) is the correct answer.

A chord of a circle passing through its centre is equal to its diameter.

3. The total number of diameters of a circle is
(a) 1
(b) 2
(c) 4
(d) uncountable number

Solution:

Option (d) is the correct answer.

The total number of diameters of a circle is uncountable.

4. By joining any two points on a circle, we obtain its
(a) radius
(b) diameter
(c) chord
(d) circumference

Solution:

Option (c) is the correct answer.

By joining any two points on a circle, we obtain its chord.

5. The longest chord of a circle is equal to its
(a) radius
(b) diameter
(c) circumference
(d) perimeter

Solution:

Option (b) is the correct answer.

The longest chord of a circle is equal to its diameter.

6. The ratio of the radii of two circles is 3: 2. What is the ratio of their circumferences?

Solution:

Given that the ratio of the radii = 3: 2

So, let the radii of the two circles be 3r and 2r respectively.

And let C₁ and C₂ be the circumference of the two circles of radii 3r and 2r respectively.

C₁ = 2 π × 3r = 6 π r … (i)

Now C₂ = 2 × 2 π r = 4 π r … (ii)

Consider, C₁/C₂ = (6 π r)/ 4 π r = 6/4 = 3/2

C₁: C₂ = 3: 2

Question from Previous Year Question Paper (MP TET 2012)

Question 1. In a concentric circle, if the length of two radii r1 (inner) and r2 (outer), then which of the following relation is true?

A. r1 + r2 = 0
B. r1 > r2
C. r1 < r2
D. r1 = r2

Solution:  C.

Two circles or more than that are said to be concentric if they have the same centre but different radii. r2 is outer radii so, it must be greater than r1.

Thanks

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